The gaseous bubble formation in crystal growth from the liquid phase under microgravity

Adv. Space Res. Vol. 11, No.7 pp. (7)185—(7)188, 1991

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THE GASEOUS BUBBLE FORMATION IN CRYSTAL GROWTH FROM THE LIQUID PHASE UNDER MICROGRAVITY Nguyen Thanh Nghi, Nguyen Thi QuyHai, Dao Due Khang and Dang Quoc Dung Institute of Physics, NCSR of Vietnam, Nghia Do-Tu Liem, Hanoi, Vietnam

ABSTRACT Some results oftheoretical and experimental investigation of formation and behaviour of gaseous inclusions during crystal growth from the liquid phase on the example of GaP:N model system have been presented.The thermodynamic analysis of gas-liquid system carried out gives the general picture of the bubble formation process and the evolution of critical gas nuclei whichare significantly influenced by the gravity. The consideration taken out hasbeen applied to some experimental crystal growth situations. Some methods for avoiding the formation and incorporation of gas bubbles into growing solid have also suggested. INTRODUCTION The problem of gaseous inclusions in semiconductor materials is of great importance for crystal growth technology, particularly in a connection with space processing. The elimination of sedimentation and Stokes flows in liquid at low g have implications for the behaviour of bubbles in such liquid. Furthermore, some recent space experiments have demonstrated that the crystals grown under microgravityfrom the liquid phase oftencontain gaseous inclusions which affect their structural perfection and homogeneity /1-3/. It should be noted, however, that at the present there is no sufficient attention paid for this problem and very little quantitave work has been performed. Therefore, questions of bubble nucleation, migration, coalescence, stability, incorporation and elimination are all of importance in reduced gravity melt processes as opposed to earth gravity processesand should be studied carefully on earth. Accordingly, in the past few years there has been a revival of interests in the study of gaseous bubble formation for various crystal growth situations /4-9/. In particular, the theoretical and experimental investigation has been carried out for bothcases of crystal growth from melt and high-temperature solution under earth and microgravity conditions on the example ofBizTe3.Bi2Se3 and Ga-Pmodel systems /7-9/. In the last work /9/ the bubble formation occurred as a consequence of the interaction of gallium oxide film GazO3 with liquid gallium generating a gaseous GazO has been considered. In this paper the further analysis of bubble formation linked with the generation of gaseous phaseby decomposition of impurities during GaP solutiongrowth is carried out for Ga:N system as an example. Some experimental results have been also presented for a comparison. THEORETICAL CONSIDERATION Thermodynamic Analysis of Gaseous bubble formation Let us consider the peculiarities of gas bubble nucleation for GaP crystal growthsystem containing the seed wafer contacting with the Ga solution. As it was shown /4,9/, the gas bubble formation in solution growth is most likely by heterogeneous nucleation on the crystal surface. The nucleation rate J then maybe expressed as:

J

=

A.exp(-i~.F5/KT)

(1)

where Kis Boltzmann’s constant andT is absolute temperature, AF is the free energy ofheterogeneous formation of critical embryo /10/:

AF

=

~Fof(9)

(2)

Here t~Fois the free energy change required to form the critical bubble in a case of homogeneous nucleation: =

16~ra3f3(P”-P’)

(3)

and f(S) = (2.cos9)(1+cos9)2/4 (4) a is the gas-liquid surface energy, is theJ~ressureinside the critical nucleus, P’ is hydrostatic pressure in the liquid at the point where the bubble is forming and U is the equilibrium contact angle between liquid drop and crystal surface in the ~“

presence of gas being considered. For-i < coaO < 1 it is givenby

cos9 = (acg-acl)/a (5) where Ocgis the surface energybetweengas and crystal, and ~ is the surface energy between crystal and liquid.For the Ga-GaP system the contact angle of gallium on a (iii) gallium phosphide surface depends on temperature and is 140, 110 and 600 at 500, 750 and i000°C,respectively/11/. The presence of oxide layers and impurities on the gallium surface may increase the contact angle which would greatly enhance bubble nucleation on GaP seed crystal surface. JASR

11:7-M

(7)185

(7)186

N. T. Nghi etal.

For the solution growth of rn-v crystals the pressure of own saturated steam is usually very low (P1< 10 ~ atm at1000°C for Ga-P system) and the gaseous phase may be formed by the evaporation of volatile impurities, either by their decomposition or by their interaction with the solution /9/. Here we will consider the example of Ga solution containing the GaN impurity. In this case of Ga-GaN system the decomposition of GaN is supposed to be responsiblefor the formation of gaseous phase:

Ga(1) + N(g)

GaN(s)

1 ~-N2(g)

=

N(g)

(6a) (6b)

1 GaN(s)

Ga(1) +

..

—

N2(g)

(6)

The equilibrium constant K~)of the reaction (6) is determined bythe ~N2 pressure and GaN concentration in Ga solution CGaN

K(T) = (PN2)~/CGaN (7) (8) PN2 = K’(T)C2GSN The critical nucleus with radius r’ must satisfy conditions of chemical and mechanical equilibrium. The mechanical and

equilibrium condition is: =

P’ + 2a/r

(9)

where P’ is the sum of hydrostatic pressure Pband totalp~~of gaseous mixture P above the solution surface: P’=P+Ph=P+pg~i g is the gravitational acceleration, h is the height andp is the density of the solution, respectively. The condition of chemical equilibrium requires that the chemical potential of each component

/4

(10) be the same inboth phases

~u’(P’,1’)= ~uN(Pu,T) (11) The result ofthis is that the gaseous pressure P~in the critical bubble is equal to its ordinaryvapour pressure over the liquid with a curvature -1/r and is determined by the ThomJ3son~Gibbsequation /6/: P” = Psexp(-2av’fRTr) (12) v’ is the molar volume of the liquid phase. P. is the saturated equilibrium pressure of N~in the considered case above a flat liquid surface. From the eqs.(8) and (12) we may find: = 2a (1

-

()

K’(T)C2GaNY’

K’(T)C2GaN~P’

RT

It can be seen from eqs.(13) and (10) that during crystallization in space the size of bubbles formed is smaller and depends only on the heating temperature. Gas Bubble Growth In our consideration the bubble growth depends on the kinetics of the reaction (6). At the same time the GaN decomposition may be, in general, limited by solute diffusion in the solution to the liquid-gas interface. Therefore, it is necessary to consider additionally the diffusion equation in the liquid phase: ôCoar’i

ä2CGaN D

=

with boundary conditions:

(14) ôC~~(0,t)

JOaN

CG 5N(00,t)

JGaN

=

1

d

—

—

=

C°G~N;

=

ôz

-

NN2(t)]

The diffusion problem (14) -(16) ha~analytical solution 1W: ldNN2 CGaN(Z,t) = C°~- — —

=

/J~1t .-~

____

D 1

[NOaN(O)

-

dNN2

-

Z erfc(~)

(16) (17)

Here NOaN(o) is the number of nitrogen impurity particles in liquid phase before the evaporation, NNZ(t) is the number of

Gaseous Bubble Formation

(7)187

N~particles-products of reaction (6), Jo.

24 is the solute mass flux and S is the reaction surface. The impurity evaporation

rate dNN2/dt can be expressedas: dNN2

KN2(C°GaN-

=

CN2)

(18)

where CNZ is the impurity concentrationin the gaseousphase: CN2 = aexp(M-AIT)

(19)

Here a is the coefficient of proportionality, M and A are constants. The growth rate of a spherical bubble is determined by the change of the tension acting on the bubble and maybe expressed as /12/: =

dt

~ 21i

+P’

-

P”)

(20)

r

Inthe realcases ofGaP growth from thin solution or under microgravity conditions Pb 0, P’< < P” and maybe neglected. Then using (8), (17) and (20) we can obtain expressions describingbubble growth. For Ga-GaN system considered above the equilibrium radius of the gas bubble at the moment t is shown to be 0 KN2[C°GaN - aexp(M ~ ~ eric_Z }2 (21) S D 2VDt req K’(T) 2a {C GaN EXPERIMENTALRESULTS AND DISCUSSION The GaP crystal growth experiments from the Ga solution were carried out by the travelling solvent method (I’SM) in a sealed ampoule and also by the isothermal LPE in the semiclosed boat. The growth temperature in both cases was about 1000°Cand Ga zone length was 2-5 mm. The GaN concentration added to the Ga melt was varied from 0.Olwt.% to lwt.%. The shape and size of gaseous bubbles and their distribution along the growing interface were investigated by an optical microscopy on the surface and cross-sectionof cleaved samples. In the GaP LPE layers grown from the Ga solution with GaN concentration above 0.OSwt.% the gaseous bubbles of regular semispherical form with different radius were observed. As it was followed from cqs.(l3) and (21), the bubbles size seems to be dependent on the GaN content in the Ga melt. Fig.1 shows the relationbetween an average radiusof thebubbles formed on the substlate at the moment of the beginning of the epitaxial growth. As seen, the bubble size r is rpughly proportional to the 1/C’GaN as predicted byeq.(13). Supposing the minimum bubble radius observed tobe a criticalr ,from the dependence presented in Fig.1 the constant of the reaction (6) K(I) can be estimated by the least square method. The value K(T) for the growth interval 1020-960°Cis determined to be 1.13.10~Pa ~1~/wt.%. The number of bubbles observed in the GaP:N LPE layers is directly dependent on the GaN content in the Ga molt (see Table 1). As it is also seen from Fig.2, the number of bubbles incorporated into GaP crystals is proportional to the GaN concentration added to the Ga melt from which they were grown. Furthermore, the structure defects originated from deteriorated substrates with the density seemingly also dependent on GaN concentration in the Ga melt (see Table 1) have been found on the GaP:N LPE layer surface. This surface deterioration, apparently, caused by the interaction between the atomic nitrogen atmosphere generated from the reaction (6a) and GaP substrates exposed to itduring heating. As it is also seen from the Table 1, for the cases of undoped growth orwith small content of GaN added to the Ga melt the gaseous bubbles and deterioration defects were notobserved in GaP epitaxial layers. From that it may be concluded that for avoiding the bubble formation and incorporation into GaP crystals dopedwith nitrogen, the amount of GaN added to the Ga meltmust be below 0.OSwt%.

r, /lm 200.

0.2

03

1.0

2

C2GaN(Wt%)2

Fig.1. Dependence ofaverage size of the bubbles obseeved in the GaP:Nlayers on the GaN content in the Ga macIt.

(7)188

N. T. Nghi et al. TABLEI Dependence of the Densityof Gaseous Bubbles and Defects in GaP:NLPE Layers on the GaN content inthe Ga Melt

No Exper.

GaN Content wt% 0

EG-87-9N EG-88-6N EG-88-1ON EG-88-12N EG-88-13N EG-88-9N EG-88.8N EG-88-7N EG-88-1N EG-88-2N EG-88-3N

Bubble Density 0 0 0 0 0 0 2 7 6 21 42

0 0 0.02 0.02 0.02 0.05 0.1 0.1 0.5 1.2

N,cni2 50

2 ~f 0

0 0 5.1& 1102 i.103 i3.i03 5.10~ i.i04

,,,/

.

0.01

Defect Density

~-2

0_i

1.0

C2GaN(Wt%)2

Fig.2 Dependence of the bubble densityin GaP:N layerson the GaN content. It has been demonstrated that in some GaP solution growth experimentsin space, the bubbles size and their distribution observed were somewhat distinguished from the earth ones /2/. Under microgravityconditions (.g 0) the bubble migration is controlled mainlyby capillary force caused by the temperature gradient in the solution. CONCLUSION We have seen that the heterogeneous bubble formation from volatileimpurities is possible in rn-v solution growth. The results of the analysis and experiments carried out in this work showed thatthe size of the bubbles and their density in LPE layer depend on the content ofvolatile impurities added to the Ga melt. it is also clear that for avoiding the bubble formation the content of these impurities must be chosen below critical level experimentally determined for concrete growth conditions and strictly controlled. It is particularly important for crystal growth experiments under microgravity conditions where the intensity of bubble formation maybe higher in comparison with earth conditions. REFERENCES 1. LL Regel and Nguyen Thanh Nghi, JAde Astronautlca, 11, 4, 155-162 (1984) 2. LL Regal and Nguyen Thanh Nghi, in: “Salyut-6” -“Soyuz” Materials Science andTechnology, Moscow Nauka 1985, p. 116 3. Nguyen Thanh Nghi and Nguyen Hoc, in: XXV COSPAR MeetIng. Abstracts of Papers, Graz, Austria 1984, 4. W.R.Wilcox, V.H.S.Kuo, 3.Cqst.Growth, 19,221(1973) 5. K.S. Bagdasarov, v.v.okinshe’vich, A.Kholov,phyLstat.soL(a), 58,317 (1980) 6. v.V.Iliukhin, v.P.Sbalimov, S.I.Budurov, P.DiCovachiov, S.A.Toncheva, in: “Salyui.6”-”Soyuz” Materials Sciences and Technology, Moscow, Nauka 1985 p.67. 7. Nguyen Thanh Nghi, A.LUshkans, V.P.shalimov, in: Proc. of VI ScientIfic Readings on Coemonautics, Moscow 1984, p.109. 8. Nguyen Thanh Nghi, A.LUshkans, T.A.Chcrepanova, J.Cqst.Res. and TechnoL 21,3,367-374(1986) 9. Nguyen Thanh Nghi, J.Cryst.Res. and Technol., 23,6, 715-722 (1988) 10. J.P.Hirth, G.M.Pound, G.R..S.Pierre, MeLTrans. 1,939(1970) 11. A.A.Berg. LH.SauI, C.R.Paola, J.Fiectrochem.Soc., 120,1558(1973) 12. J.V.Lcvinskij, in: Materials and Processes of Space Technology, Mocow 1980, p.26. 13. J.I.Frenkel, .JETF,16,29(1946)

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